Daily Archives: 2011年7月18日

Scott-Blair论流变学的两个目的和吵架

回郑融老师邮件的时候我脑中突然想到的一个问题是,为什么我感到我学习的流变学跟他的关于注塑成型的书所代表的流变学差别很明显?顺便推荐一下郑老师的书:

[AMAZONPRODUCT=364221262X]

我们现在对真正的流动还是描述不清楚

我所说的区别是,注塑成形给我的感觉是流体力学。而我做的流变学经常是统计力学。流体力学和统计力学估计是很多流变学初学者感觉横在自己面前的两座大山。两者各不相同但都很深。流体力学的主要花招在于flow,各种不同形状的流道的各种挤压、拉伸流还有什么二次流,以至于你光用个powerlaw fluid都够你玩了。而统计力学则由于考虑了分子或粒子,而且是一堆。相互作用问题涉及多体,所以就算不流动都难死人,经常是平均场。因此统计力学里考虑流动至多就是dissipation-fluctuation theory(DFT,其思想说白了就是应力松弛),一超过线性理论就很够呛。聚合物结构流变学,发展了这么多年了,到现在还是不能统一地把剪切流和拉伸流一起描述好,说明“统计力学的流变学”经不起“流体力学的流变学”的折腾。好多理论,只限于一种flow,一旦换一种flow就立马歇菜。毕竟,按许元泽老师曾经私下总结,“我们现在对真正的流动还是描述不清楚”。

当然,什么时候也不可能说我们“描述清楚”了的,所以上面这种话如果脱离上下文来理解就会变成一句大话。

我回郑老师的信是为了Scott Blair的事,关于流变学的上述“两座大山”Scott-Blair在J. Sci. Instrum.1940, 17, 169)里也总结过。虽然字不少,但行云流水,不妨全引:

There are two reasons for measuring rheological (flow and deformation) properties of industrial materials. On the one hand, a property hitherto unassessed is measured in the hope that it may be found to correlate with some quite different characteristic of the product. In some cases there are theoretical reasons for supposing such a connexion: in others the process is quite empirical. As examples, we may quote the determinations of the viscosity of dilute suspensions of flour in water, which were at one time frequently made as an index of the baking quality of the dough, or the connexion between the condition of flocculation and hence of the flow properties of thin clay pastes with the tilth of field soisls (i.e. potentialities as seed-beds).

More frequently, on the other hand, the rheologist attempts to imitate in a quantitative and objective way some measurement which has long been made subjectively by the expert in manufacture, This is not so much in order to replace men by machines as to give the expert a standard against which to compare his judgements and to ensure that different experts measure the same properties under the same names, although in some few cases the subjective judgement has tended to be altogether replaced in course of time.

Scott-Blair接下来进一步引用普朗克的话,把整个一研究论文写得好像一篇essay一样亲切。这一点后面再说。上面这段引文的主要意思是说,流变学研究有两个目的,一个是研究物质的结构-性能关系,一个是为了找到准确、简洁的表征方法。前者其实是物理化学,因此就会动用到统计力学。因为物理化学就是研究万物的结构-性能关系的科学。有的人喜欢说“凝聚态物理”,那也可以。因为化学涉及到的物质尺度和pVT区间确实就大致上是这个。否则说到底粒子物理和宇宙学也属于“结构-性能”关系的研究了。至于另一个目的其实是测量学,所以做法是通过现象学的总结提取出最有表征作用的参数。例如你可以不需要知道整个直线方程,只需要知道个斜率就可以了——这一知识是通过大量观察发现重要的东西其实就是斜率来确定的。所以既然谈到“测量”,那就有测不准原理了,就要引用普朗克的话了。

普朗克的那段很著名的话其实也应验在我当前的研究中。有一种流变学其实并不流也不变,而是通过给样品施加小到可以忽略的形变来测试样品,并把测试结果理解为样品不受形变时的性质,例如线性粘弹性范围的应力松弛和动态粘弹谱,这些做法的理论是DFT。但是面对像螺杆挤出这种情况,你再去做什么应力松弛那就显得很笨拙很可笑。所以要做非线性流变学,各种各样的阶跃剪切、拉伸……这些测试的问题就在于Scott-Blair说的“different experts measure the same properties under the same names”的问题了。你要测样品流动时的性质,你就得让样品流动。而流动改变结构,结构又反过来影响流动。因此,“流动”事实上本来是很容易成为一种重现性非常差的实验条件的。我们的多年以来的幸运其实是来自样品结构的简单(例如单分散线形柔性聚合物),结构一复杂点儿,time-dependence就来了,触变性就来了,different experts所measure的就不一定是the same properties under the same names了,于是就各自为政了。这也是为什么半个世纪之后的Barnes在写Thixotropy — a review(J. Non-Newt. Fluid Mech. 1997, 70, 1)的时候说Scott Blair自称“the whole subject [of thixotropy] is so very new”但同时引用了八十多篇相关论文。这就算哪怕有800篇论文,由于没有形成一种统一的公认客观的表征套路,因此大部分都是各自为政,不comparable。

因此,虽然凝聚态物理那一块的流变学现在特别热门,但是现象学这一块的流变学一直都很重要。我感觉人们很容易去鄙视一切现象学,因此刚才关于现象学的流变学我多说一点儿。

Barnes在他的review里还说:

Readers with an interest in the historical derivation of scientific expressions are directed to Scott-Blair [10], p.52. All Scott-Blair’s books were written as personal memoirs and are very evocative of the man himself for those who knew him.

其中文献[10]是下面这本书:

[AMAZONPRODUCT=B0007J1J9A]

我已经买下了,估计要下个月才能ship到广州。同时我还买了Scott-Blair的另一本书:

[AMAZONPRODUCT=B0000CHRBO]

这应该是一本更哲学的书。在Journal of Nervous & Mental Disease 1956, 123, 499上有关于这本书的书评(算是“跨界”了),让我在看到原书前就先了解大致的内容:

Most scientists do not even try to distinguish with accuracy between what is real in a measured dimension and what is but a result of abstract logical classification. He describes briefly some of the essential features, the similarities and differences, of spatial, psychological and physical dimensions of space and of time. The author points out that the scales and concepts of measurement cannot be the same in all science and that, e.g., physics and psychology (including psychoanalysis) need their own specific definition of dimension and measuring units.

Scott-Blair其实是鼓吹要为不同的研究对象发明不同的dimension。这在流变学中确实是常见的,我们常常不对真实时间作图,而是对一个“dimensionless”的时间作图。我们有很多dimensionless的量,例如DeWePeCa等,它们经常取代传统时间或频率作为图的横坐标,这一切也许会让其他物理学背景但刚进入流变学的人抓狂,但确是流变学家们的智慧所在。可是,Scott-Blair的这一说法在当时被批为mysticism,批评的原文看不到了,但Scott-Blair好像很不快,在Br. J. Appl. Phys. 1951, 2, 60上回应了这种指责。半个世纪的流变学发展证明这种dimension,只要是很好地反映了问题实质的那些,都获得了广范的应用,完全没有带来mysticism,反而帮我们去除了原有的mysticism,是好的science。